Existence of positive solutions to integral equations with weights
Existence of positive solutions to integral equations with weights
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DOI：
10.1016/j.aml.2019.106089
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
Qianqiao Guo;Qian Wang
中科院分区：
文献类型：
--
作者：
Qianqiao Guo;Qian Wang
In this paper, we are concerned with the existence and non-existence of positive solutions to the following integral equation related to the sharp Hardy–Littlewood–Sobolev inequality f q− 1 (x)=∫ Ω K (x) f (y) K (y)| x− y| n− α d y+ λ∫ Ω f (y)| x− y| n− α− β d y, f≥ 0, x∈ Ω¯, where q> 1, 1< α< n, 0< β< n− α, Ω is a smooth bounded domain, K (x) is positive continuous in Ω¯. For K≡ c o n s t, β= 1, the existence and non-existence of positive solutions to the equation has been studied by Dou and Zhu (2019). This paper is devoted to the case K (x)⁄≡ c o n s t. We want to point out that the weight function will bring difficulty when estimating the energy of the energy functional according to the integral equation.
